A device for performing that type of inspection is known, in particular from document (FR 2 567 058). However, the means that it implements suffer from major drawbacks in applications where machining time constitutes a non-negligible factor in the cost price of the pieces being machined. With the known device it is necessary to stop the crank shaft rotating and to put the apparatus manually into contact with the crank pin that is to be inspected. Even if the operation of putting the inspection apparatus into contact with the crank pin were to be automated, and likewise the taking out of contact thereof, it would still be necessary to stop the rotating crank shaft in a determined angular position. That known apparatus therefore gives rise to a loss of productivity when grinding crank pins.